Advertisements
Advertisements
प्रश्न
Prove the following:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Advertisements
उत्तर
sin 2A = λsin 2B
∴ `(sin 2"A")/(sin 2"B") = lambda/1`
∴ `(sin2"A" + sin2"B")/(sin2"A" - sin2"B") = (lambda + 1)/(lambda - 1)`
∴ `(2sin((2"A" + 2"B")/2)*cos((2"A" - 2"B")/2))/(2cos ((2"A" + 2"B")/2)*sin((2"A" - 2"B")/2)) = (lambda + 1)/(lambda - 1)`
∴ `(sin("A" + "B")*cos("A" - "B"))/(cos("A" + "B")*sin("A" - "B")) = (lambda + 1)/(lambda - 1)`
∴ tan(A + B) · cot(A – B) = `(lambda + 1)/(lambda - 1)`
∴ `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`.
APPEARS IN
संबंधित प्रश्न
Prove the following:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Prove the following:
`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x2 + y2 = ____________.
The value of sin 163° cos 347° + sin 167° sin 73° is ______
`sqrt3 sin15^circ + cos15^circ` = ______
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
The value of cos 15° is ______.
The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.
If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.
If cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to ______.
If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
The value of cot 70° + 4 cos 70° is ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
